What is the solution for 4(d^2y)/(dx^2)-12(dy)/(dx)+5y=0 ?

The solution for 4(d^2y)/(dx^2)-12(dy)/(dx)+5y=0 is y=c_{1}e^{(5x)/2}+c_{2}e^{x/2}

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4(d^2y)/(dx^2)-12(dy)/(dx)+5y=0

4 \frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 5 y = 0

y = c_{1} e^{\frac{5 x}{2}} + c_{2} e^{\frac{x}{2}}

Solution steps

4 \frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 5 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{5 x}{2}} + c_{2} e^{\frac{x}{2}}

y = c_{1} e^{\frac{5 x}{2}} + c_{2} e^{\frac{x}{2}}

4 y^{^{''}} + y^{^{'}} + \frac{1}{16} y = 0

y^{^{'''''}} + 16 y^{^{''''}} + 80 y^{^{'''}} = 0

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = \frac{1}{2}, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} - 9 \frac{d y}{d x} + 18 y = 0

y^{^{''}} + 5 y^{^{'}} + 4 y = 0, y^{^{'}} (0) = 1, y (0) = 1

What is the solution for 4(d^2y)/(dx^2)-12(dy)/(dx)+5y=0 ?
The solution for 4(d^2y)/(dx^2)-12(dy)/(dx)+5y=0 is y=c_{1}e^{(5x)/2}+c_{2}e^{x/2}